Topological light fields in free space: fundamentals and applications

Abstract

The incorporation of topology into physical dimensions of light introduces global and quantized characteristics that give rise to a new class of optical fields with enhanced robustness and functionality. Topological light fields are defined by nontrivial topological invariants, such as winding numbers, linking numbers, and skyrmion or Hopf indices, encoded in phase singularities, polarization textures, or spatiotemporal structures, providing a unifying framework for understanding and engineering complex optical structures. In this review, we present an overview of the fundamentals and applications of topological light fields in free space. We first classify topological light according to two-dimensional cross-profile topology, three-dimensional spatially-propagated topology, and spatiotemporal topology, and summarize the underlying physical principles, generation methods, and characterization techniques for representative structures, including optical vortices, vector beams, skyrmions, optical knots, Möbius strips, Hopfions, and spatiotemporal optical vortices. We then survey recent advances in applications enabled by topological light fields, covering high-capacity and robust optical communications, topological quantum entanglement, optical storage, precision optical metrology, and multidimensional optical trapping. Finally, we discuss key challenges and emerging opportunities in this rapidly evolving field. This review aims to provide a detailed roadmap for both fundamental research and technological development in free-space topological photonics.